Yolanda trades 100 uncorrelated strategies. She has 100 assistants each flip a coin. Yolanda goes Long 1% of her account for each coin that lands Heads, and goes Short 1% of her account for each coin that lands Tails. The strategies are uncorrelated because the coins are independent. Zack trades 5000 uncorrelated strategies. He has 5000 assistants each flip a coin. Zack goes Long 0.02% of his account for each coin that lands Heads, and goes Short 0.02% of his account for each coin that lands Tails. The strategies are uncorrelated because the coins are independent. Clearly Zack has more uncorrelated strategies than Yolanda. But I don't think he has a higher overall return/risk figure, particularly when commissions and slippage are included. I think the statement above, in bold, needs further qualification.
horribilicus, the systems first need to show good backtesting results to qualify at all. I wouldn't trade any system, no matter how good I'd feel about it, if it hasn't been backtested or forward tested for substantial time. Yes, trading single system at a time might be more profitable, if another system can choose which system to trade when, with results better than running all simultaneously. I'm speaking about automated approach, if you can do that manually, ok.
i don't think man's statement needs further qualification at all. your example at trying to disprove that assertion, does the opposite actually. per your example, zack in fact does have a higher overall return/risk figure, particularly when commissions and slippage are included. aside from the fact that zack has less exposure on a per trade basis, the volatility of yolandas returns will be greater, and that the odds of 5000 vs. 100 systems all becoming correlated on the same day are much lower; you also have the fact that zack is trading smaller, thus his slippage will be reduced. if they both pay per share commissions, their commsissions will be equal. your assumption that increased frequency = increased slippage and commissions is just wrong. i'd pick zack over yolanda any day of the week to manage my money. well, that is, until i found that he was flipping coins.
Thank you for pointing out an ambiguity. Since ET doesn't allow edits to the original message after 1 hour, the clarification is shown below. I have added the phrase "every Monday", the additions are in blue text. By the way this is a perfect example of the Axiom of Oddiduro! (shown in this post) Every Monday, Yolanda trades 100 uncorrelated strategies. Every Monday, she has 100 assistants each flip a coin. Every Monday, Yolanda goes Long 1% of her account for each coin that lands Heads, and goes Short 1% of her account for each coin that lands Tails. Every Monday, Yolanda makes 100 trades, one for each of the strategies she trades. The strategies are uncorrelated because the coins are independent. Every Monday, Zack trades 5000 uncorrelated strategies. Every Monday, he has 5000 assistants each flip a coin. Every Monday, Zack goes Long 0.02% of his account for each coin that lands Heads, and goes Short 0.02% of his account for each coin that lands Tails. Every Monday, Zack makes 5000 trades, one for each of the strategies he trades. The strategies are uncorrelated because the coins are independent. Clearly Zack has more uncorrelated strategies than Yolanda. But I don't think he has a higher overall return/risk figure, particularly when commissions and slippage are included. I think the statement above, in bold, needs further qualification.
putting in those qualifiers doesn't make the argument any better. it doesn't change the return/risk profiles for either trader, independetly or comparatively. you obviously know enough about statistics to use some terms, and the way you used them isn't wrong, but your interpretations are. you need to look outside basic stat theory like stantionarity and correlation for understanding problems like defining return/risk profiles. specifically, probablility and game theory are much more applicable here. here's a big hint for understanding why your example is flawed, look up and understand variance: how it applies to frequency and odds, how it's affected by bet sizing, and how it would affect the volatility of an equity curve (a graphical way of viewing return/risk) under different scenarios. the easy way to do this, if you know how to code, is to just plot some payout distributions for each of your examples and look at the stddev of returns for each trader. if you can do that, it should become self-evident.
If you perform the very experiments that you suggest, you will find that Zack does not have a superior risk/reward profile.
so u flip coins to make market decisions? ingenious, u might want to try excel's random number generator. saves your fingers from getting all tired
further qualification: adding uncorrelated nonEdge to nonEdge will still be nonEdge. the whole topic is extremely simple. i have a system with a sharpe of 2+ and i have now one other with a sharpe of 2+ on paper trading which in backtest correlated 0.3 with the first one. i can hardly believe that anybody on this board or in the entire world better to say, would NOT turn on system 2, just because there is already one other ... i would say there is not very much more to it. the real issue is that additonal systems which do not correlate are hard to find. development as such is damned hard, but now you have the hurdle that you would like to lean where you know you can find something. and you have to resist and start from more or less scratch somewhere else. THAT is the issue with multisystems and IMHO it is the only one. everything else is beating around the bush. a trading operation is a development operation not an executing office. once you have not developed something new for more than 12 months ... that raises a flag. at least it does for me.
ill second that, development of uncorrelated trading strats is extremely difficult. One of the things ive found was to analyse the type of market which fucks up your current system and then make one which expliots the market during those time periods. For example if your trading an ADX/ATR/breakout system then whipsaw markets will cause the majority of your drawdowns Yet stochastics or %williams R will work well in a whipsaw market or one thats trading in a range. The key is making a system which links the two together. For example you may want to see any characteristics that occur just before you enter into the type of market that is profitable for either teh trend following or stochastic system. You may define anything less than 20 ADX as a whipsaw market, or one which is lacking in price and volume movement adn use that framework to decide which system you use. Its a complicated process and usually only trial and sometimes very costly error will yield you the system.
i personally don't need to do the experiments because i understand the basic math needed to figure it out. i suggested them for you to try because you just weren't understanding a very basic concept: risk of ruin. perhaps you'll understand this better: the probability of yolanda blowing out the first day is: (.5)^100 the probability of zack blowing out the first day is: (.5)^5000 zack's risk is lower. there is no argument here. this is basic probability. you're wrong dude, period.